Well, I have seen lots of responses that I would have posted myself, so I won't repeat anything. However, I have three daughters, and the 13 year old has a friend spending the night tonight so I asked their opinions on this:
My DD: She used to really want one because she thought they were cute and cool. She liked the different kinds of jewelry available, and liked the idea of showing it off to her friends that spend the night, or when she goes to the pool. She changed her mind when she heard comments from boys her age, feeling that they saw belly-button rings as a sign of a girl being sexy and "willing". She said she thought it portrayed the wrong image; she didn't want to be seen as being "that way". (she is kind of a feminist at heart)
Friend: Was allowed to make the decision to get one or not, and her mom took her to get it done. (Mom has one and had no trouble with it at all, she got it as a reward for losing 30 pounds. 15 yo sister has one, but it got infected, finally healed, but is crooked.) When mom took her, they refused to pierce the 13 y.o. They said that "any reputable body artist won't do anyone under the age of 15", and then only if a parent is present, because they feel 13 is "too young to properly care for it, and may not be doing it for the right reasons." She says she still wants one, but doesn't know if she will get it done when she is 15 or not, because of what her sister went through.
Bottom line: Both still think they look cute, love the different jewelry, but are going to wait and think on it to see if it is something they want in the long run.
Julie